Application of Calculus in Non Continuous Physical Systems

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Calculus is traditionally based on the assumption of continuity, yet its application in physics persists despite the discontinuous nature of matter. The discussion highlights the tension between the belief that calculus is inappropriate for analyzing systems like gravitation and electromagnetism, and the counterargument that calculus has proven effective in these areas. Critics of the discontinuity argument assert that the behavior of atoms does not negate the utility of calculus in modeling physical phenomena. Furthermore, no specific examples were provided to demonstrate that calculus leads to erroneous results in these contexts. The debate underscores the complexity of applying mathematical principles to the physical world.
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In the mathematics of Calculus, a basic requirement is that the system or function should be continuous. Until the discovery that matter is discontinuous, applying Calculus in Physics was reasonable. But why is it still applied almost everywhere in physics ? Won't such applications produce erroneous results ?
 
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Which matter is discontinuous? Do you have specific examples in mind?
 
SteamKing said:
Which matter is discontinuous? Do you have specific examples in mind?

Does it mean that some form of matter is continuous ? Matter, as we all know, is made up of atoms. So it is discrete and discontinuous. So I believe that application of Calculus is inappropriate in areas like Gravitation, Electromagnetism and Nuclear Physics.
 
Well, I can't argue with your beliefs, but I reject them. Application of the calculus to the problems you mention has been quite successful. You assume that atoms behave independently regardless of circumstances. Your assumption that the calculus can deal only with mathematically continuous systems is also faulty. You also have not provided any examples, according to your hypothesis, that application of the calculus has provided faulty results when used to analyze physical phenomena.
 
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